Measuring statistically the deviation of
measurement outcomes from the ideal value of quantum measurements on
given quantum states, the variance plays an important role in quantum
physics and quantum information theory. The first uncertainty
relation known as the Heisenberg's uncertainty relation was given
in terms of the variance [1]}, [2]}, which
describes the restrictions on the accuracy of measurement results of two
or more noncommutative observables. Since then, many efforts are
made to find tighter and state-independent lower bounds on such kind
of uncertainty relations [3]}, [4]}, [5]}.
In order to study the restriction between the uncertainties for two
or more observables, the notion of the uncertainty region is also
put forward and characterized [6]}, [7]}.
